For months now thousands of troops from the US-led coalition - most of them American - have been hard at work in the forbidding terrain of eastern Afghanistan hunting followers of the hardline Taleban movement they toppled three and a half years ago.

They are also after members of another group - Hezb-e Islami Gulbuddin.

Its leader has declared similar aims to the Taleban - to fight a jihad or holy war to push the Americans out of Afghanistan and unseat the government of President Hamid Karzai.

Few believe they have any chance of success but they are still causing a lot of damage.

Bloody period

There is always an increase in fighting with the arrival of spring - which melts the snow in the high passes and narrow defiles the militants use to slip back and forth - in many cases from the Pakistani tribal areas just across the border.

It is not their spring offensive, it is our spring offensive

Brig Gen James Champion

It was the same story in the 1980s during the Soviet occupation.

But US commanders had been suggesting this one would be much quieter. That they finally had the militants on the run.

Instead, it has turned out to be one of the bloodiest periods in the past three years.

In some areas, there have been almost daily clashes with militants.

An estimated 1,000 people have been killed in the past six months, most of them militants but also about 50 US troops.

But the Americans say it is the Taleban who are coming off worse.

Brig Gen James Champion is deputy commander of US operations for the whole of Afghanistan.

"There are increases in clashes because we are instigating the clashes. It is not their spring offensive, it is our spring offensive."

'Personal power'

Yet although small in number compared to casualties in Iraq, more US troops have died in the past few months than in the same period last year.

Hamid Karzai's Taleban reconciliation plans have been hazy

And American troops and their commanders who operate in the areas where the Taleban are concentrated are more cautious about writing them off.

Col Gary Cheek is in charge of US forces in eastern Afghanistan. "I don't think comments about the demise were misguided. But it is a slow process.

"We have a small number of higher-level leaders who are very committed, more about personal power than ideology. I doubt we will see them quit the cause.

"They will maintain a level of insurgency for the future but it will become less and less of a threat to the sovereignty of Afghanistan."

But Col Cheek believes it important not to "mislead ourselves" by simply chasing the enemy.

"We need to put an effort into friendly forces, in training police, working with government, rebuilding infrastructure so the government gets the confidence of the people."

Eligible

Col Cheek has also been instrumental in initiating another tactic in his area over the past six months - trying to persuade insurgents to give up fighting.

Some say the US coalition troops are getting bogged down

It has become known as the "Allegiance" programme.

All but the 50 to 100 most senior Taleban figures are eligible.

In return for backing President Karzai's government, they are allowed to return home and will not be arrested.

But it is a fairly ad-hoc programme that was begun as a stop-gap measure ahead of the Afghan government's own initiative.

That initiative when it came caused confusion.

Professor Sibghatullah Mojaddedi, head of the Afghan government's newly formed Reconciliation Commission, appeared to offer an amnesty to the Taleban leader Mullah Mohammed Omar and Gulbuddin Hekmatyar, leader of Hezb-e Islami.

It took some time before President Karzai made clear there was no such offer. And anyway, Mullah Omar said he was not interested.

Although small groups of Taleban are turning themselves in - like former commander Malim Jan - there is no mass defection.

Debilitating

As the spring fighting season gave way to summer, the situation remained uncertain.

Mullah Mohammad Omar turned down an amnesty suggestion

There were some steps forward - for example, the decision of several moderate Taleban members to stand for September's parliamentary elections.

On the other hand, there were some serious steps back.

In June, a bomb exploded at a mosque in Kandahar during the funeral of an anti-Taleban Islamic scholar - 20 people were killed. It was the worst bombing attack in the past three years.

The Taleban initially claimed responsibility, but then denied it.

However, many analysts believe they were involved in some way.

Other attacks continue, meaning there is little hope of the Americans being able to withdraw.

Some say they are bogged down. The history of insurgencies shows it takes very few people to pin down a very large number of troops.

There are thought to be no more than 2,000 active Taleban militants and perhaps several hundred followers of Gulbuddin Hekmatyar.

But even if the number of defections increases, the Taleban insurgency and the debilitating insecurity it brings could carry on for a long time yet.